Full Idea
The nominalist finds that standard semantics shackles him to first-order languages if, as nominalists are wont, he is to make do without abstract higher order objects.
Gist of Idea
The nominalist is tied by standard semantics to first-order, denying higher-order abstracta
Source
Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.166)
Book Reference
'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.166
A Reaction
Aha! Since I am pursuing a generally nominalist strategy in metaphysics, I suddenly see that I must adopt a hostile attitude to higher-order logic! Maybe plural quantification is the way to go, with just first-order objects.